**3. Cup Mixing Temperature and RMSD**

The temperature of cup mixing is defined to discover the thermal mixing inside the chamber. The velocity weighted average temperature is most appropriate for convection flow than space averaged temperature. The temperature of cup mixing, and averaged temperature based on area are given as [34]

$$T\_{\rm Cap} = \frac{\iint \hat{V}(\mathbf{X}, \mathbf{Y}) \, T(\mathbf{X}, \mathbf{Y}) d\mathbf{X} d\mathbf{Y}}{\iint \hat{V}(\mathbf{X}, \mathbf{Y}) d\mathbf{X} d\mathbf{Y}} \tag{20}$$

where *V* <sup>ˆ</sup>(*<sup>X</sup>*,*<sup>Y</sup>*) = √*U*<sup>2</sup> + *V*<sup>2</sup> and

$$T\_{\text{avg}} = \frac{\iint T(\mathbf{X}, \mathbf{Y}) d\mathbf{X} d\mathbf{Y}}{\iint dX d\mathbf{Y}} \tag{21}$$

The root-mean square deviation (RMSD) is deduced to calculate the degree of temperature uniformity in all considered cases. They are deduced based on temperature of cup mixing and average temperature based on area as follows:

$$RMSD\_{T\_{\rm cap}} = \sqrt{\frac{\sum\_{i=1}^{N} \left(T\_i - T\_{\rm Cap}\right)^2}{N}} \tag{22}$$

$$RMSD\_{T\_{avg}} = \sqrt{\frac{\sum\_{i=1}^{N} \left(T\_i - T\_{avg}\right)^2}{N}} \tag{23}$$

The greater values of RMSD point out poorer temperature regularity in the chamber and vice versa. Moreover, RMSD cannot exceed one because the dimensionless temperature differs between zero and one. These parameters are estimated by the gained values of flow and thermal fields in the same computational code.
